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If the least common multiple (LCM) of two numbers is 36 and their greatest commo

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Question: If the least common multiple (LCM) of two numbers is 36 and their greatest common divisor (GCD) is 6, what can be inferred about the product of the two numbers?

Options:

  1. It is 216.
  2. It is 72.
  3. It is 36.
  4. It is 6.

Correct Answer: It is 216.

Solution: 

The product of two numbers is equal to the product of their LCM and GCD: 36 * 6 = 216.

If the least common multiple (LCM) of two numbers is 36 and their greatest commo

Practice Questions

Q1
If the least common multiple (LCM) of two numbers is 36 and their greatest common divisor (GCD) is 6, what can be inferred about the product of the two numbers?
  1. It is 216.
  2. It is 72.
  3. It is 36.
  4. It is 6.

Questions & Step-by-Step Solutions

If the least common multiple (LCM) of two numbers is 36 and their greatest common divisor (GCD) is 6, what can be inferred about the product of the two numbers?
  • Step 1: Understand the terms LCM and GCD. LCM (Least Common Multiple) is the smallest number that is a multiple of both numbers. GCD (Greatest Common Divisor) is the largest number that divides both numbers without leaving a remainder.
  • Step 2: Identify the values given in the question. The LCM is 36 and the GCD is 6.
  • Step 3: Use the relationship between the product of two numbers, their LCM, and their GCD. The formula is: Product of the two numbers = LCM * GCD.
  • Step 4: Substitute the values into the formula. So, Product = 36 (LCM) * 6 (GCD).
  • Step 5: Calculate the product. 36 * 6 = 216.
  • Step 6: Conclude that the product of the two numbers is 216.
  • Least Common Multiple (LCM) – The smallest multiple that is exactly divisible by two or more numbers.
  • Greatest Common Divisor (GCD) – The largest positive integer that divides two or more numbers without leaving a remainder.
  • Relationship between LCM and GCD – The product of two numbers is equal to the product of their LCM and GCD.
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